Revealing mistake: When they're trying to get rid of the bat at the cabin, they hold up a sheet to force it out of the door, however when they reach the door, you can see the bat being pulled up with string or wire.
Revealing mistake: Watch the scene where they're headbanging and the tape keeps going out. You can see where they splice the scene in because the trees change in the background instantly.
Revealing mistake: After the roof blows off the cabin, the hail starts falling inside the cabin. It is fairly obvious that the hail is just being poured onto the cabin. Its most noticeable just after the hail starts falling on the cabin, there is a shot taken from inside the cabin you can tell by the night sky and some of the trees outside that there is no hail in the distance.
Revealing mistake: When Mike crashes the truck into the movie marquee, some of the light bulbs explode well before the truck hits them.
Revealing mistake: When Mike is on his way to go vote and he falls down the hill, he gets to a spot where it isn't steep enough for him to be moving fast. If you look closely, you can tell that the editors of the movie fast-forwarded it to make it look like he is rolling down the hill really fast.
Revealing mistake: When Mike slips and falls down the hill you can clearly see that he is pushing himself down as he goes.
Revealing mistake: When it starts hailing inside the cabin, you can obviously tell that the night sky has wrinkles in it, revealing that this "sky" is a black curtain in a stage.
Revealing mistake: At the very end of the film, when Chris Farley is stuck to the airplane when it's in the air, you can easily notice that he has been replaced with a dummy. You can easily tell by seeing his legs are too flexible and skinny.
Revealing mistake: Could the scene when the big rock knocks down the cabin be any faker? You can easily tell that the cabin and the rock are miniature models.
Answer: A major police department would probably not allow modifications to an official vehicle, even if it was assigned permanently to a particular officer, due to safety or insurance concerns. That said, many departments do use high performance or exotic vehicles seized during crimes under various forfeiture laws. Most times these are for promotional purposes, but I do know of a Florida department that used a souped-up Dodge Hemi-Charger painted in standard department livery for traffic enforcement.